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4. Crime and pollution in major metropolitan areas are public bads but get better as one moves farther from the city. At the same time, commuting costs (private) also increase with distance from the city. Suppose the cost of crime and pollution is 1/(d^2), where d is distance to city and the cost of commuting is equal to the round-trip distance, 2d. Assume there are no other costs involved. A worker is choosing her optimal location. Assume the closest she can live is 0.1 miles and the farthest is 100 miles.
a. What is the total cost for this worker as a function of distance?
b. Where will the worker choose to locate [hint: what is the marginal cost]?
c. If the city fully compensates this worker for her damage from crime and pollution, where would she choose to live?
d. A tempting response to a public bad (such as an airport or superfund site) is to compensate households based on their exposure to these bad things. What effect does this have on overall levels of exposure? [Note: this is different than compensating households for damage related to past exposure to pollution or other public bads.]
e. Instead of compensating for damage, suppose instead the city and employers introduced programs to subsidize commuting (such as subsidized parking, EZ-pass subsidies, or commuting allowances). What effect would this have on worker’s location decisions?